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Planar Fabry-Perot-based ultrasound sensors are highly sensitive for their small element size when interrogated with focused Gaussian beams. Here we announce the development of two models that can characterize the circumstances under which a Bessel interrogation beam provides sensitivity superior to that of a Gaussian beam, extending photoacoustic imaging depth without compromising sensor directivity.

In this manuscript, we propose a novel transmissive metasurface capable of dynamically controlling the phase of linear polarized waves at the microwave regime. The local phase control is dynamically obtained with the help of individually controlled varactors and PIN diodes inserted in the metasurface unit cell. Moreover, we show that the proposed metasurface can be used to generate zero- and first-order microwave Bessel beams with high efficiency (90%).

Acoustic radiation force (ARF) induced Shear wave elasticity imaging (SWEI) is a noninvasive method to characterize pathological tissues. Conventionally, ARF is generated by focused beam with limited depth of focus. Supersonic shear imaging (SSI) uses multiple push-beam foci to achieve larger depth of field (DoF) elastograms. Here, we propose a SWEI method based on Bessel apodized ARF to generate larger DoF with lower energy. As a result, Bessel elastogram in gel phantom shows 19% higher contrast-to-noise ration (CNR) and 95% lower energy than SSI. Furthermore, Bessel elastogram in porcine liver shows 61% higher signal-to-noise ratio (SNR) and 56% lower energy than SSI.

Limited-diffraction beams (LDBs) such as Bessel beams and X waves have been studied since late 1980s and early 1990s respectively. These beams have a large depth of field and were applied mainly for medical imaging. (For example, LDBs can maintain a narrow -6-dB beam width of about 2.54 mm in water from the surface of the transducer to more than 200 mm depth at a frequency of 2.5 MHz.) In these applications, LDBs were not focused in order to have a large depth of field. In this paper, both focused zeroth-order and higher-order LDBs were studied for ultrasound therapy applications. The advantage of using focused LDBs is that their focal areas and shapes can be systematically controlled to treat tumors of various sizes. In the study, Bessel beams of 2.5 MHz were produced with a 50 mm diameter transducer. The Bessel beams were focused at 50 mm depth and the sizes and shapes of the focal areas were controlled by the scaling parameter and the order of the Bessel beams. To increase the total transmitting power and reduce the number of elements of the transducer needed to produce the Bessel beams, the amplitudes of the lobes of the Bessel beams can be quantized at the surface of the transducer. Results show that with the focused Bessel beams, the sizes of the focal areas increase with the increase of the Bessel scaling parameter, and higher-order Bessel beams produce a perforated focus area.

Accoustic in-homogeneities within biological tissues are known to degrade image quality in elastography. Previous work has demonstrated the potential of Bessel apodized acoustic radiation force (ARF) beams in elasticity reconstructions. Bessel offers advantages, such as enlarged depth-of-field (DOF) and high diffractive immunity over conventionally focused pushes. In this study, we demonstrate Bessel ARF's ability to generate broader bandwidths for phase velocity recovery. Performance was evaluated against matched supersonic shear imaging (SSI) experiments on commercial and custom viscous phantoms. Bessel's ability to “heal”, after being disrupted by an obstacle makes it a potential candidate for developing better phase reconstruction in the presence of heterogeneity.

The data of infections by Covid-19 is modeled through the integer-order Bessel functions that have been parametrized in according to the morphology of data. In particular, the modeling is focused on official data belonging to UK, Germany, Italy and Netherlands. The free parameters of model have been coherently linked to data. Interestingly, it was seen that a "silent period" with the lowest cases of infections play a relevant role for new pandemics as well as the apparition of new strains, such as the most recent "delta-variant".

Robust implementations of special functions have been a concern in many scientific areas, from electromagnetics to statistics. For example, the kernel of the Helmholtz equation in a boundary integral formulation is based on Hankel functions, or the Matern covariance in statistics depends on the functions Gamma and modified Bessel. Traditionally these special functions are implemented using known asymptotic expansions on certain critical intervals. The strategy we introduce here is to replace asymptotic expansions with neural network (NN) models taking advantage that NNs can be provably considered to be universal approximators. This approach facilitates a plethora of operations previously inaccessible. For instance, high-order derivatives of a neural network model preserve the accuracy of the trained model and, as such, can be more reliable than derivatives of asymptotic expansions. Implementations of series expansions may be computationally prohibitive and prone to numerical errors in regions where they do not converge sufficiently fast. In the current work, we develop neural network models to be a stand-in for special functions, focusing on the Bessel functions of the first and second kind, and corresponding derivatives. Special functions may require different series expansions for different ranges of the argument. We showcase a strategy for using the same neural network model over any interval within the domain of definition of the function, that would otherwise require different asymptotic expansion representations.

Zero-order terahertz Bessel beams are diffractom-free. Therefore, unlike the traditional Gaussian beam CT, the terahertz zero-order Bessel beam used in terahertz CT imaging can improve the depth of field of the imaging system. At the same time, the imaging system has high lateral resolution. Bessel beam CT was used to scan a variety of samples at the same time and the reconstruction results were obtained. The reconstructed sections and three-dimensional structures of the scanned samples were clearly seen.

A custom aspheric axicon lens for corneal water content sensing, operating from 220 to 330 GHz, was evaluated with spherical, dielectric shell targets. The lens consisted of a hyperbolic back surface and conical front surface with a 25-degree axicon angle. An 8 mm radius of curvature, 1 mm thick, air backed dome was placed in the beam path and S11 acquired at numerous axial offsets between dome and axicon. The data was normalized by equivalent radius of curvature metallic spherical reflectors. Fits to reflectivity data ranged from e = 4.1 and t = 0.89 mm and e= 4.16 and t = 0.885 for lens-tip to shell-apex distances of 34 mm and 25 mm respectively. The results suggest that Bessel beam illumination may relax axial alignment constraints in THz imaging of cornea. © 2021 European Union

While it is known that the Milky Way is a barred spiral galaxy, the precise locations of the spiral arms are not easily derived by observations, because of the Sun's location in the disk plane. The Galactic disk is large (radius of ~15 kpc) and the high dust obscuration in the disk plane limits distances from optical astrometry to a few kpc. The Bar and Spiral Structure Legacy (BeSSeL) programme and the Japanese VERA project measured parallaxes and proper motions, via VLBI maser astrometry, for more than 200 high-mass star-forming regions out to a distance of 20 kpc. BeSSeL has provided a new parametrisation of the spiral arm structure and determined the fundamental Galactic parameters. The BeSSeL results presented here have been published in [1].

The paper considers a new class of polynomial filters which is an extension of the Bessel (Thomson) filters. This extension is achieved considering the difference of two weighted Bessel polynomials. The weight of the subtracted polynomial is including the multiplier a n the choice of which defines the class of resulting filters. When a n = 0 one obtains the transfer functions of regular Bessel (Thomson) filters. When a n =1 one obtains the Stokes filters. The Stokes filters are faster than Bessel filters but have larger step response overshoot. Using the range of −1 n ≤ 2 one obtains the stable filters with controllable step transient response overshoots. The upper border for a n is defined by the stability condition of higher order filters, the low border is defined by the non-monotonicity conditions.

Recently, the diffraction of an electromagnetic plane wave by multiple rectangular apertures was solved by the Kobayashi potential method, and matrix equations with double infinite integrals in their elements were derived [1] . To obtain the numerical results for the physical quantities such as the radiation pattern and aperture field, the integrals whose integrands consist of four Bessel functions and two trigonometric functions must be computed with the desired accuracy. Therefore, we propose a fast and accurate integration method and the related algorithm. The integration region is divided into several finite and infinite regions, and in the infinite regions, the asymptotic expansion of the Bessel function is applied to convert the integrals into simple infinite integrals containing only elementary functions [2] . We assume all of the aperture sizes are the same (2 a × 2 b ) for simplicity. The following formula is an example of integrals in the infinite region.

A recent investigation [1] has developed an exact analytic solution of the Maxwell equations for an antenna which is characterized by an electric current which flows azimuthally on an infinitely thin spherical shell with a density that scales with the angle of spherical elevation. The resulting form of the electro-magnetic (EM) fields can be expressed as a simple product of a small number of elemental functions, including spherical Bessel functions and standard harmonic functions, without the need for any infinite series in the final expressions. These EM fields are truly exact for all space, both interior and exterior to the spherical electric current shell, since no approximations are invoked involving the relative spatial scales of the sphere diameter, the EM wavelength, or the distance to an observation point.

The spherically layered media theory is widely used in electromagnetic wave scattering problems. In the theory, the numerical computations of Bessel functions are unstable when the argument is small, the media is lossy, or the function's order is large. This paper addresses problem. We first define the renormalized reflection and transmission coefficients which have more clear physical meanings and ordinary magnitude of values. Then, logarithmic derivative of Racatti-Bessel funtions is used to calculate the renormalized single-interface reflection and transmission coefficients. Finally, recursive formulas of the renormalized multi-interface reflection and transmission coefficients are derived. In the proposed method, the stable computations of the layered media theory are simply reduced to iteratively calculate the ratio of Bessel functions of adjacent orders. The validity and stability of this method have been verified by numerical tests.

In this study, we use Scanning Field Emission Microscopy (SFEM) combined with a miniature electron energy analyzer known as a Bessel box to measure electron energy spectra emitted from a sample. Previous studies using SFEM have revealed that the work function (ϕ) of the material under study has a significant role to play in the formation of the signal intensity. Hence, in order to understand the role of ϕ in greater detail, a sample of W(110) (ϕ = 5.25 eV) and a sample of Cs deposited on W(110) (ϕ ≈ 1.7 eV) were investigated. STM images show that the Cs covered surface has a speckled appearance indicating small Cs islands. The electron energy loss spectra obtained (which are the first using the Bessel box in SFEM) show differing structure in the elastic peak region. Monte Carlo (MC) simulations including quantum mechanical "bouncing" have been carried out. The results are consistent with MC simulations of the electrons escaping from the tip-sample junction.

In this paper, we investigate the applications of Higher Order Bessel Beams with temporal modulation of Orbital Angular Momentum (OAM) for maritime applications. Examples include the creation and detection of HOBBIT beams at unprecedented time scales and power densities. Results are also presented for sensing of rotating fog clouds and nonlinear interactions in water.

Bessel beams of the zeroth order are notorious for characteristic of having diffraction-less focal zone. Due to this property they became desirable for a number of laser micromachining applications, such as Bragg grating inscription, microchannel forming, photopolymerization and more [1] . By means of spatial light modulators or diffractive optical elements Bessel like beam variations with shaped transverse intensity distribution can be obtained which also proved beneficial in glass cleaving, for example [2] . Higher order Bessel beams also known as Bessel vortex beams also have interesting properties like carrying orbital angular momentum [3] . A combination of Bessel vortices of different topologies allows to form high width/depth ratio beams with complex transverse intensity distribution [4] , [5] . Such beams can be realized with geometrical phase elements which are manufactured by inscribing birefringent nanograting inside the bulk of fused silica [6] . By controlling retardance and the local angle of nanograting one can manufacture numerous beam shaping elements.

It is well known that a light beam transforms into a hollow light cylinder after passing along one of the optical axes of a biaxial crystal. This optical phenomenon is known as conical refraction (CR) and fascinates researchers for almost two centuries. The characteristic features of CR find a number of practical applications in optical manipulation, polarization metrology, and singular optics to name a few [1] . However, these seem to be hindered by the lack of intuitive understanding and prediction of the CR transverse intensity pattern. This problem was partially solved by expressing the CR field as a superposition of the Bessel-Gaussian (BG) beams [2] .

The propagation and interaction of unconventional Airy beams in nonlinear media permits the creation of multiple photo-induced waveguiding structures which are interesting for the development of all-optical interconnects [1] , [2] . Such complex light-induced structures, different from those induced by Gaussian beams, result from the unique profiles and peculiar characteristics of Airy beam (diffraction-free, self-healing). Bessel beams share similar features with Airy beams and have been studied in the past and recent years for example in a self-focusing nonlinear medium [3] , [4] where soliton-like, breathing and self-trapping properties have been observed. However, the studies are limited only to a single Bessel beam in a quadratic electro-optic response, and nonlinear interactions of Bessel beams is not studied.

Conference Name: 2021 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) Date of Conference: 21-25 June 2021 Here, we introduce the first controlled nanofabrication capability in the bulk of silicon wafers. We exploit smart use of Bessel beams and demonstrate "in-chip" nano-structuring with features lower than 250 nm.

Bessel beams have gained prominence due to their diffraction-free propagation and self-healing properties [1] . The zeroth-order Bessel beam has maximum intensity at its center and has found many applications, including optical trapping and bio-imaging. On the other hand, higher-order Bessel beams have a node due to a phase singularity and carry orbital angular momentum (OAM). Over the past years, Bessel beams have been generated by using different approaches, namely by Fourier transforming a narrow circular beam with a lens, by using axicons and with holographic beam shaping techniques. The need to miniaturize optics has led to efforts towards the on-fiber generation of Bessel beams. The successful attempts include the fabrication of a customized annular-core fiber along with a polymer lens [2] , or modifying the end of the fiber to an axicon profile with chemical or lithographic methods [3] . These techniques have limited capability on generating Bessel beams with on-demand optical parameters and are only focused on creating zeroth-order Bessel beams from optical fibers.

In this paper, semi analytical solutions for velocity field and tangential stress correspond to fractional Oldroyd-B fluid, in an annulus, are acquired by Laplace transforms and modified Bessel equation. In the beginning, cylinders are stationary, motion is produced after t = 0 when both cylinders start rotating about their common axis. The governing equations solved for velocity field and shear stress by using the Laplace transform technique. The inverse Laplace transform is alternately calculated by Stehfest's algorithm using “MATHCAD” numerically. The numerically obtained solutions are in the form of modified Bessel's equations of first and second kind and satisfying all the imposed physical conditions. Finally, there is a comparison between exact and obtained solutions. It is observed that semi analytical technique and exact technique are approximately the same and satisfy imposed boundary conditions. Through graphs, the impact of physical parameters (relaxation time, retardation time kinematic viscosity, and dynamic viscosity) and fractional parameters on both velocity and shear stress is observed.

Novel diffractive elements are presented to produce zero-order Bessel beams in the terahertz (THz) band. First, diffractive elements are designed as phase plates to change the direction of the incident Gaussian beam. Then, they are fabricated by the emerging three-dimensional printing technology. Last, zero-order Bessel beams are generated by the diffractive elements at 0.3 THz. To verify the feasibility of this approach, the generated zero-order Bessel beams are monitored and compared with the ones generated by the axicons. The comparison confirms that the diffractive elements can produce Bessel beam effectively and efficiently. In addition, the diffractive elements are applied to introduce zero-order Bessel beam to a THz reflection imaging system. A resolution test phantom is imaged by the THz reflection imaging system with zero-order Bessel beam and a conventional THz reflection imaging system. The results indicate that the THz reflection imaging system with Bessel beam offers a significantly extended depth of field and high anti-interference capability.

The process of acousto-optic (AO) interaction of Gaussian-like beam and backward Bessel acoustic beam in acoustically transversely isotropic crystals was investigated. AO diffraction on vertically-polarized (SV-) acoustic wave was studied that allowed involving diagonal components of permittivity tensor into AO-process. It was established that due to the mentioned diagonal components there can be realized isotropic diffraction of Gaussian-like light beam into Bessel light beam with high diffraction efficiency. The proposed scheme of AO diffraction is of interest for obtaining Bessel light beams from Gaussian ones with the possibility of dynamic tuning of their parameters.

We numerically investigate the propagation and interaction of Bessel beams in a photorefractive (PR) nonlinear medium. By varying Bessel beam parameters and the PR nonlinearity, complex multi-channel structures can be photoinduced by single or two counter-propagating (CP) Bessel beams. These results pave the way towards all-optical interconnects.

Love waves in the cylindrically piezoelectric substrate loaded with a conductive polymer are studied analytically. The governing equations can be transformed into the general form of Bessel equation and three dimensional Laplace equation. The coupled wave equations are solved and dispersion equations are obtained by using continuity conditions on the interface and the boundary conditions on the surface of the structures. The relationship between phase velocity and frequency can be calculated and presented. The effects of viscosity on phase velocity can be figured and discussed.

In this paper, the minimum mean square error (MMSE) channel estimation for intelligent reflecting surface (IRS) assisted wireless communication systems is investigated. In the considered setting, each row vector of the equivalent channel matrix from the base station (BS) to the users is shown to be Bessel K distributed, and all these row vectors are independent of each other. By introducing a Gaussian scale mixture model, we obtain a closed-form expression for the MMSE estimate of the equivalent channel, and determine analytical upper and lower bounds on the mean square error. Using the central limit theorem, we conduct an asymptotic analysis of the MMSE estimate, and show that the upper bound on the mean square error of the MMSE estimate is equal to the asymptotic mean square error of the MMSE estimation when the number of reflecting elements at the IRS tends to infinity. Numerical simulations show that the gap between the upper and lower bounds are very small, and they almost overlap with each other at medium signal-to-noise ratio (SNR) levels and moderate number of elements at the IRS.

Scattering of Bessel beams can be matter of great interest in many practical areas such as near-field radar cross section (RCS) measurement, ground penetrating radar (GPR) and optical microscopy. In this contribution, we explore the advantages of performing inverse scattering through Bessel beams to obtain better results when compared to standard inversion approaches dealt with standard incident fields such as plane waves, current filaments or fields radiated by dipoles/loops in tridimensional imaging. Preliminary numerical assessments are given towards metallic scatterers by exploiting the well-known standard back-propagation technique.

Bessel-Gauss beams (BGBs) have been widely investigated in optics in the paraxial approximation, under the frame of a scalar wave theory. Such approximations no longer hold in the microwave/millimeter-wave range, where the vectorial nature of electromagnetic fields cannot be neglected, and experimental realizations of BGBs are still lacking. In this work, we discuss the generation of BGBs through a fully vectorial electromagnetic approach. The field derivation and the numerical evaluation of a BGB are first illustrated. A possible scheme for realizing such solutions is outlined, thus paving the way for the first experimental realization of BGBs at microwave frequencies.

We consider a wireless free space optical (FSO) communication system. The FSO link is assumed to follow the gamma-gamma distribution. It is shown in literature that the probability density function (PDF) of the gain of FSO link has complicated form, it is in the form of modified bessel function. Due to its complicated nature, the analytical expressions of FSO communication system has very high computational complexity. In this paper, for a FSO link, an approximate expression in terms of series expansion for PDF of the gain of FSO link is derived. Further, it is shown that the derived approximate expression is accurate and easy to deal. The performance analysis of the FSO based communication system is performed in terms of bit error rate by using the derived PDF expression.

This paper proposes a method to compute the coupling factor of single and multi-layered coils having a square, hexagonal, or circular geometry, placed center to center to each other, such that there is no lateral or angular misalignment, and only vertical misalignments are of interest. Existing methods involve using 2D / 3D electromagnetic solvers, elliptical integrals, Bessel function, magnetic vector potential, or a combination of these methods. All these methods increase computational complexity and are not in a compact form. The calculation of the coupling factor requires the computation of mutual inductance and the self-inductance of the coils. The self-inductance of single-layered coils is calculated using Modified Wheeler's eq. and the self-inductance for multi-layered coils is calculated using a combination of Modified Wheeler's eq. (for the inductance of each layer) and elliptical integrals (for mutual inductance between layers). The mutual inductance of single and multi-layered coils is derived based on the series expansion of Neumann's eq. with an addition of a factor to reduce the maximum error from 37% to 6.64%. A side length transformation eq. is derived and proposed for equivalent coil transformation from a hexagonal coil to a circular coil or vice versa. The method proposed here requires only geometric quantities of the coils for the computation of mutual inductance. Simulation and experimental results showed excellent agreement with the proposed model of separation distances greater than the inner radius of the transmitter (Tx) or receiver (Rx) coil (whichever has a smaller inner radius). For simulation results, an error of up to 5% was seen for single-layered coils and an error of up to 6.64% was seen for multi-layered coils. For experimental results, the error was under 5% for double-layered air coils and 8.1% for single-layered coils with a ferrite core at separation distances greater than the inner radius of the coils. Hence, the coupling factor can be computed accurately with the proposed model at separation distances greater than the inner radius of Tx or Rx coil.

A reflection metasurface that can generate non-diffraction Bessel beams and achieve anomalous reflection with high efficiency at 5.8 GHz is proposed in this paper. The unit it utilizes has excellent amplitude and phase characteristics, greatly facilitating the construction of the proposed metasurface and laying a solid foundation for the improvement of efficiency. According to non-diffraction theory and anomalous reflection law, two metasurfaces are designed for comparison. The simulation results show that the designed metasurfaces successfully realize the non-diffractive beam with a focusing distance of 126 mm (2.44 λ 0 ), and can bend the normally reflected wave to the direction 10° from the +z direction in a vertical plane 45° away from the +x direction. The average efficiency of the metasurface within the focusing range is as high as 84.5%, thus could be used as radio energy transmission, telecommunication multiplexing and accurate detection devices.

In optics and acoustics, a particular solution of the wave equation, created by the superposition of Bessel beams of the same frequency, permits obtaining a stationary wave field with a static envelope in space. These solutions are called Frozen Waves and could have multiple potential applications. In this paper, the analysis of frozen waves using different levels of discretized finite aperture annular radiators is presented. The produced fields with these discretized radiators are compared with the field produced by a continuous finite aperture with the same radial distribution calculated to produce a single focus. The discretized radiator was based on a Bessel transducer varying the number of rings for each studied condition. Even though the acoustic frozen field is improved for the most numbers of rings (50 rings transducer), results with the 20 rings transducer show a similar pressure pattern at the focus. This would facilitate experiments for our future applications in ophthalmic ultrasound therapy.

In this article, we propose methods for the generation of surface plasmon polaritons (SPPs), both carrying orbital angular momentum, and conventional ones, using vortex Bessel beams, and also investigate the propagation of SPPs along flat and cylindrical conductors. The possibility of their practical application is discussed and the first experimental results are presented.

We demonstrate generation of "droplet" Bessel beams using semiconductor laser and an axicon with rounded tip. Interference of Bessel and Gaussian wave fronts leads to cancellation of side lobes of Bessel beam.

The paper considers a new class of filters with transfer functions providing equal step-response overshoots for all filter orders. This class of filters is derived using Bessel polynomials. The proposed procedure indicates also that Bessel filters are part of a wide class of polynomial filters with prescribed step-response overshoot. The example considered in the paper describes the set of filters, from second to eight order, all having the step-response overshoot equal to 5%. The paper presents the transfer functions of the filters, their frequency responses in the passband and stopband, special features of these responses in the transition zone, and gives the calculated step-response transients.

Bessel beams have attracted considerable interests due to their intriguing non-diffracting and self-healing properties. An electronically-engineered metamirror is designed for the flexible control of Bessel beams over a broad frequency band ranging from 9 GHz to 12 GHz. Several configurations are presented to illustrate the non-diffracting features of Bessel beams. The self-healing property is verified by placing a metallic obstacle in the propagation path of the Bessel beam. Owing to the flexible manipulation capabilities, wide bandwidth and highefficiency properties of the reconfigurable metamirror, the proposed Bessel beam generation device opens the door to potential applications for focusing and wireless power transmission.

A complete framework for the shielding effectiveness (SE) evaluation of the undermoded enclosure in reverberation chamber is presented in this work. For this purpose, the generalized extreme value distribution is used to describe the undermoded field in the enclosure. To estimate the parameters of the generalized extreme value distribution, frequency stirring is adopted to provide independent samples which are determined by the Pearson correlation coefficient and threshold related to the number of independent samples of mechanical stirring in reverberation chamber, and then L-moments method is used to estimate the parameters based on the independent maximums extracted from independent samples in the stirring bandwidth. According to a rough knowledge of the parent distribution converging to Bessel K and some assumptions, SE of the undermoded enclosure is finally derived.

A movement of harmonically modulated beam of electrons of other charged particles moves near an obstacle is known to be accompanied by the diffraction radiation (DR). We study DR for a beam flowing between two circular nanotubes of the same metal and geometry. The electromagnetic field of such a beam is a slow H-polarized wave, which propagates along the beam trajectory and decays exponentially off the trajectory. To analyze DR, we use the boundary conditions and the field expansions in the local polar coordinates supplemented with the addition theorems for Bessel functions. This leads to a matrix equation for the field expansion coefficients. Its conversion to the Fredholm second-kind form guarantees controlled accuracy in the computation of the far and near field patterns, which demonstrate resonance behavior. As we have shown, deviation of the beam trajectory from the central, i.e. symmetric, position is accompanied with the excitation of additional resonances. This phenomenon can be exploited in the design of non-invasive optical-range beam position nanomonitors.